Question

Write a code for Matlab that solve for the root of the equation " sin2x = 0 ", using Newton method.

Answer 1

The Matlab Code is given below in the table.

Matlab Code

clc clear all % declare the function as needed f = @(x)sin(2*x); % declare the differentiation of the above function df = @(x)2*cos(2*x); fprintf('The function is: f(x) = %s\n', char(f)) % max number of iterations to be used to calculate the root max_iter = 50; iter = 1; % declaring the error tolerance tol = 1e-5; % choosing the initial root as guess x_prev = 0.1; x = 0; err = 1; while(true) % calculating the next root x = x_prev - f(x_prev)/df(x_prev); % calculating the error err = abs(x - x_prev); % check whether the error is less than tolerance if(err < tol) break; end % check whether the iteration exceeds max number of iteration if(iter >= max_iter) error('Sorry! The Program can not calculate the root.') end % assign previous root to current root x_prev = x; % incerement the iteration cout iter = iter + 1; end % print the final calculated root fprintf('Final calculated root using newton method is %.4f\n', x) % print number of iterations taken fprintf('Total number of iterations used = %d\n', iter)

OUTPUT